Well, in order to avoid being confused if you are and android developer, this is just a reminder that hopefully will makes things more clear.
Typically, SDK Tools are platform independent whereas Platform tools, obviously, support the features of the latest Android Platform. Build Tools gather tools that will produce your signed Apk.
you can get more detailed information from the official documentation.
Roughly, SDK tools include all the tools that you need to develop for android;
That includes the SDK manager (to download android SDKs), development tools such as AVD (android virtual devices), Image tools (such as draw 9 patch), Debugging tools (such as ddms), monkey runner and so…
It is not an exhaustive list of course. You can open the folder on your machine to get all of the tools.
These tools are updated for each new android sdks release and is backward compatible. The platform tools include for instance ADB which is a bridge that allows you to communicate with your android device or emulator. ADB has to know how to communication with the Android version that is hosted on your device.